Emily found the volume of this cone to be 24.5 What would the volume of this cylinder be with the same radius and height?
i-can
Page xx of your INB
Write down this problem on your
READY RECALL SHEETBe prepared to explain your answer
if you are called on.
find the volume of a hemisphere with a radius of 14 meters.
V = 24.5
V = ?Same radius &height as cone
V = 3 x 24.5V = 73.5
RE- Try this CHALLENGE question:
Cone is 1/3 the volume of the cylinder. The area left would be 2/3 of the cylinder’s volume.
V = πh = π5 = 94.2477… = 94.2
Page xx of your INB
i-can
Get into your Groups
We will be using the foldable we made
last time.
find the volume of a hemispherewith a radius of 14 meters.
SPHERES
Why don’t we ever see planets shaped like cylinders or cones?
Everywherewe look in space, planets—and even stars like our sun—are shaped like spheres.Why is that?
Of course, not every object we observe in space is a sphere. Asteroids, comets, and even very small moons often have weird, rough shapes. These objects are too small—and their gravities too weak. For them, the sphere-making process never begins.
The answer is gravity. For a large body in space, gravity pulls every point on the surface equally toward its center. Over time, gravity molds the body into the only possible shape that could form from such a process—a sphere!
LETS TRY SOME PROBLEMS
List the radius, diameter, and circumference for each problem. Use the π key on the calculator and round to the tenths place.
Radius:
Diameter:
Circumference:
Radius:
Diameter:
Circumference:
Radius:
Diameter:
Circumference:C = 2πr C = 2πr C = 2πr
h =
6m
FINDING THE VOLUME OF A
SPHERE
ACTIVITYLet’s place a sphere in a cylinder with the same radius and height.
How much of the cylinder do you think the sphere uses?
V (cylinder) = πh 301.6
r=4mSOOOO…. If the Volume of a Cylinder is about 301.6, what is your guess for the
Volume of the Sphere with the same radius and height?
(write it down and show your partner).
Volume of a Sphere Demonstration Videohttps://www.youtube.com/watch?v=8jygxFuLoCk
The volume of the sphere is of 301.6 201.1
DERIVING THE VOLUME OF THE SPHEREh
eig
ht radius
Volume of a Sphere = (Volume of a Cylinder)
= π
= π
= π
= π
INB NOTEBOOK ACTIVITY
Write the parts of
the figure.
Write the formula and find the volume of the
example shown.
V = π
V = π
V = π
= 904.7786… 904.8
r
LETS TRY SOME PROBLEMS
Calculate the volume for each sphere. Use the π key on the calculator. Round decimals to the nearest tenth. Write out each formula.
HEMISPHERE
Talk in your groups…
Remind each other what a hemisphere is.
Discuss how the volume of a sphere is different than the volume of a hemisphere?
= (π)
V(hemisphere) = (V sphere)
V(hemisphere) = π
= π
Day 1 – Integer operations, PEMDAS, evaluating10.5 Volume of a Sphere
i-can find the volume ofa hemisphere with a radiusof 14 meters.
Number 14 on your Homework